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Introduction to Magnetohydrodynamics 2nd Revised edition [Mīkstie vāki]

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(University of Cambridge)
  • Formāts: Paperback / softback, 572 pages, height x width x depth: 246x174x30 mm, weight: 1020 g, Worked examples or Exercises; 15 Tables, black and white; 30 Halftones, black and white; 90 Line drawings, black and white
  • Sērija : Cambridge Texts in Applied Mathematics
  • Izdošanas datums: 22-Dec-2016
  • Izdevniecība: Cambridge University Press
  • ISBN-10: 131661302X
  • ISBN-13: 9781316613023
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Introduction to Magnetohydrodynamics 2nd Revised editionPalielināt
  • Formāts: Paperback / softback, 572 pages, height x width x depth: 246x174x30 mm, weight: 1020 g, Worked examples or Exercises; 15 Tables, black and white; 30 Halftones, black and white; 90 Line drawings, black and white
  • Sērija : Cambridge Texts in Applied Mathematics
  • Izdošanas datums: 22-Dec-2016
  • Izdevniecība: Cambridge University Press
  • ISBN-10: 131661302X
  • ISBN-13: 9781316613023
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9781316613023.html
Keywords:
"Magnetohydrodynamics (MHD) plays a crucial role in astrophysics, planetary magnetism, engineering and controlled nuclear fusion. This comprehensive textbook emphasizes physical ideas, rather than mathematical detail, making it accessible to a broad audience. Starting from elementary chapters on fluid mechanics and electromagnetism, it takes the reader all the way through to the latest ideas in more advanced topics, including planetary dynamos, stellar magnetism, fusion plasmas and engineering applications. With the new edition, readers will benefit from additional material on MHD instabilities, planetary dynamos and applications in astrophysics, as well as a whole new chapter on fusion plasma MHD. The development of the material from first principles and its pedagogical style makes this an ideal companion for both undergraduate students and postgraduate students in physics, applied mathematics and engineering. Elementary knowledge of vector calculus is the only prerequisite"--

Recenzijas

Review of previous edition: ' an excellent book, which provides a refreshing introduction and a welcome addition to the MHD literature.' A. M. Soward, Journal of Fluid Mechanics Review of previous edition: 'The language of this book is simple, vivid, yet fully scientific. It is a real pleasure to read worth recommending, not only to students, but also to everyone who is interested in MHD, particularly to theoreticians who, as a rule, know almost nothing about metallurgical applications of MHD.' Applied Mechanics Review Review of previous edition: 'Like other texts in the series, the typography is easy on the eyes and the price easy on the purse. All in all, a wonderful introduction to the subject and more!' Stanley A. Berger, Physics Today Review of previous edition: ' a thorough introduction to conducting fluid mechanics an excellent and informative book that can be well recommended.' S. W. H. Cowley, Contemporary Physics Review of previous edition: 'The author writes lucidly and maintains the reader's interest in several ways: he formulates arguments provocatively, sometimes as paradoxes; he provides apt quotations; he points to exciting applications; and he enlivens his text with historical snippets It is written with love, and in a completely consistent style.' Paul H. Roberts, SIAM Review Review of previous edition: 'The book is unique in bringing together a number of diverse topics [ It] makes for rewarding reading, and I recommend it to all students of MHD, no matter what their persuasion. It would be an excellent textbook for students with interest in the engineering applications, but also will serve as a perfect complementary text for an introductory plasma MHD course.' Elena V. Belova, American Journal of Physics 'The rich scholarship presented in this monograph is a result of the author's ongoing study of these concepts This careful documentation, also provided for modern technology, gives the reader an exceptional glimpse into this field.' J. W. Jerome, MathSciNet 'This book is at once a useful basic textbook introducing the elements of electromagnetism and fluid dynamics and, at the same time, an informative research monograph targeting professional researchers in industry and academia.' K. Alan Shore, Optics & Photonics News

Papildus informācija

Comprehensive textbook prioritising physical ideas over mathematical detail. New material includes fusion plasma magnetohydrodynamics.
Preface to the Second Edition xv
Preface to the First Edition xvii
Part I From Maxwell's Equations To Magnetohydrodynamics 1(120)
1 A Qualitative Overview of MHD
3(24)
1.1 What Is MHD?
3(3)
1.2 A Brief History of MHD
6(1)
1.3 From Electrodynamics to MHD: A Simple Experiment
7(10)
1.3.1 Some Important Parameters in Electrodynamics and MHD
8(1)
1.3.2 Electromagnetism Remembered
8(3)
1.3.3 A Familiar High School Experiment
11(6)
1.4 A Glimpse at the Astrophysical and Terrestrial Applications of MHD
17(7)
Exercises
24(3)
2 The Governing Equations of Electrodynamics
27(30)
2.1 The Electric Field and the Lorentz Force
27(2)
2.2 Ohm's Law and the Volumetric Lorentz Force
29(2)
2.3 Ampere's Law and the Biot-Savart Law
31(3)
2.4 Faraday's Law and the Vector Potential
34(3)
2.5 An Historical Aside: Faraday and the Concept of the Field
37(3)
2.6 Maxwell's Equations
40(7)
2.6.1 The Displacement Current and Electromagnetic Waves
41(2)
2.6.2 Gauges, Retarded Potentials and the Biot-Savart Law Revisited
43(4)
2.7 The Reduced Form of Maxwell's Equations for MHD
47(2)
2.8 A Transport Equation for the Magnetic Field
49(1)
2.9 A Second Look at Faraday's Law
49(7)
2.9.1 An Important Kinematic Equation
50(1)
2.9.2 The Full Significance of Faraday's Law
51(2)
2.9.3 Faraday's Law in Ideal Conductors: Alfven's Theorem
53(3)
Exercises
56(1)
3 A First Course in Fluid Dynamics
57(55)
3.1 Different Categories of Fluid Flow
57(12)
3.1.1 Viscosity, the Reynolds Number and Boundary Layers
58(4)
3.1.2 Laminar Versus Turbulent Flow
62(3)
3.1.3 Rotational Versus Irrotational flow
65(4)
3.2 The Navier-Stokes Equation
69(1)
3.3 Vorticity, Angular Momentum, and the Biot-Savart Law
70(4)
3.4 The Vorticity Equation and Vortex Line Stretching
74(6)
3.5 Inviscid Flow
80(5)
3.5.1 Kelvin's Theorem
80(1)
3.5.2 Helmholtz's Laws
81(2)
3.5.3 Helicity Conservation
83(2)
3.6 Viscous Flow
85(6)
3.6.1 The Dissipation of Energy
85(1)
3.6.2 The Burgers Vortex
86(2)
3.6.3 The Prandtl-Batchelor Theorem
88(3)
3.7 Boundary Layers, Reynolds Stresses and Elementary Turbulence Models
91(7)
3.7.1 Boundary Layers
91(2)
3.7.2 Turbulence and Simple Turbulence Models
93(5)
3.8 Ekman Layers and Ekman Pumping in Rotating Fluids
98(3)
3.9 Waves and Columnar Vortices in Rotating Fluids
101(9)
3.9.1 The Taylor-Proudman Theorem
102(1)
3.9.2 Inertial Waves, Helicity Transport and the Formation of Taylor Columns
103(3)
3.9.3 Inertial Wave Packets, Columnar Vortices and Transient Taylor Columns
106(3)
3.9.4 A Glimpse at Rapidly Rotating Turbulence
109(1)
Exercises
110(2)
4 The Governing Equations of MHD
112(9)
4.1 The MHD Equations and Key Dimensionless Groups
112(4)
4.2 Energy Considerations
116(1)
4.3 Maxwell's Stresses and Faraday's Tension
117(3)
4.4 A Glimpse at Alfven Waves
120(1)
Part II The Fundamentals Of Incompressible MHD 121(184)
5 Kinematics: Advection, Diffusion and Intensification of Magnetic Fields
123(21)
5.1 The Analogy to Vorticity
123(1)
5.2 Diffusion of a Magnetic Field
124(1)
5.3 Advection in Ideal Conductors: Alfven's Theorem
125(3)
5.3.1 Alfven's Theorem
125(1)
5.3.2 An Aside: Sunspots
126(2)
5.4 Helicity Invariants in Ideal MHD
128(3)
5.4.1 Magnetic Helicity
128(2)
5.4.2 Minimum Energy states
130(1)
5.4.3 Cross Helicity
131(1)
5.5 Advection Plus Diffusion
131(10)
5.5.1 Field Sweeping
132(1)
5.5.2 Flux Expulsion
133(3)
5.5.3 Azimuthal Field Generation by Differential Rotation: The Ω-Effect
136(1)
5.5.4 Stretched Flux Tubes and Current Sheets
137(2)
5.5.5 Magnetic Reconnection
139(2)
5.6 Field Generation by Flux-Tube Stretching: A Glimpse at Dynamo Theory
141(1)
Exercises
142(2)
6 Dynamics at Low Magnetic Reynolds Numbers
144(41)
6.1 The Low Magnetic Reynolds Number Approximation
145(1)
6.2 The Suppression of Motion
146(19)
6.2.1 Magnetic Damping
146(2)
6.2.2 The Damping of a Two-Dimensional Jet
148(1)
6.2.3 The Damping of a Vortex
149(6)
6.2.4 The Damping of Turbulence at Low Rm
155(4)
6.2.5 Natural Convection in a Magnetic Field: Rayleigh-Benard Convection
159(6)
6.3 An Aside: A Glimpse at the Damping of Turbulence at Arbitrary Rm
165(3)
6.4 The Generation of Motion
168(10)
6.4.1 Rotating Fields and Swirling Motion
168(3)
6.4.2 Swirling Flow Induced between Two Parallel Plates
171(3)
6.4.3 Flows Resulting from Current Injection
174(4)
6.5 Boundary Layers and Associated Duct Flows
178(5)
6.5.1 Hartmann Boundary Layers
178(3)
6.5.2 Pumps, Propulsion and Projectiles
181(2)
Exercises
183(2)
7 Dynamics at High Magnetic Reynolds Numbers
185(43)
7.1 Alfven Waves and Elsasser Variables
187(3)
7.2 Finite-Amplitude Alfven Waves and the Conservation of Cross Helicity
190(2)
7.3 Colliding Alfven Wave Packets and a Glimpse at Alfvenic Turbulence
192(3)
7.4 Magnetostrophic Waves
195(2)
7.5 The Energy Principle for Magnetostatic Equilibria in Ideal Fluids
197(12)
7.5.1 The Need for Stability in Plasma Confinement
198(3)
7.5.2 The Stability of Static Equilibria: A Variational Approach
201(5)
7.5.3 The Stability of Static Equilibria: A Direct Attack
206(3)
7.6 An Energy-Based Stability Theorem for Non-Static Equilibria
209(6)
7.7 The Chandrasekhar-Velikhov Instability in Rotating MHD
215(9)
7.7.1 The Magnetic Destabilisation of Rotating Flow
216(4)
7.7.2 The Energy Principle Applied to Rotating MHD
220(2)
7.7.3 The Destabilising Influence of an Azimuthal Field
222(1)
7.7.4 The Destabilising Influence of an Axial Field
223(1)
7.8 From MHD to Euler Flows: The Kelvin-Arnold Theorem
224(2)
Exercises
226(2)
8 An Introduction to Turbulence
228(49)
8.1 An Historical Interlude
229(4)
8.2 The Structure of Turbulent Flows: Richardson's Cascade
233(6)
8.3 Kinematic Preliminaries (for Homogeneous Turbulence)
239(16)
8.3.1 Correlation Functions and Structure Functions
239(5)
8.3.2 Spectral Analysis
244(5)
8.3.3 The Special Case of Statistically Isotropic Turbulence
249(6)
8.4 Kolmogorov's Theory of the Small Scales
255(4)
8.5 The Karman-Howarth Equation
259(7)
8.5.1 The Karman-Howarth Equation and the Closure Problem
259(3)
8.5.2 The Four-Fifths Law
262(2)
8.5.3 Spectral Dynamics
264(2)
8.6 Freely Decaying Turbulence
266(11)
8.6.1 Saffman versus Batchelor Turbulence: Two Canonical Energy Decays Laws
266(5)
8.6.2 Long-Range Interactions in Turbulence
271(2)
8.6.3 Landau's Theory: The Role of Angular Momentum Conservation
273(2)
8.6.4 Problems with Landau's Theory and Its Partial Resolution
275(2)
9 MHD Turbulence at Low and High Magnetic Reynolds Numbers
277(28)
9.1 The Growth of Anisotropy at Low and High Rm
277(4)
9.2 Loitsyansky and Saffman-like Invariants for MHD Turbulence at Low Rm
281(5)
9.3 Decay Laws for Fully Developed MHD Turbulence at Low Rm
286(2)
9.4 The Spontaneous Growth of a Seed Field at High Rm: Batchelor's Criterion
288(3)
9.5 Magnetic Field Generation in Forced, Non-Helical Turbulence at High Rm
291(6)
9.5.1 Different Categories of Magnetic Field Generation
292(2)
9.5.2 A Kinematic Model for Field Generation in Forced, Non-Helical Turbulence
294(2)
9.5.3 The Role of the Magnetic Reynolds and Magnetic Prandtl Numbers
296(1)
9.6 Unforced, Helical Turbulence at High Magnetic Reynolds Numbers
297(10)
9.6.1 Ideal Invariants and Selective Decay
298(2)
9.6.2 Taylor Relaxation
300(1)
9.6.3 Dynamic Alignment and Alfvenic States
301(4)
Part III Applications In Engineering And Materials 305(94)
10 The World of Metallurgical MHD
307(10)
10.1 The History of Electrometallurgy
307(3)
10.2 An Overview of the Role of Magnetic Fields in Materials Processing
310(7)
11 The Generation and Suppression of Motion in Castings
317(34)
11.1 Magnetic Stirring Using Rotating Fields
317(15)
11.1.1 Casting, Stirring and Metallurgy
317(3)
11.1.2 The Magnetic Teaspoon
320(2)
11.1.3 Simple Models of Stirring
322(3)
11.1.4 The Role of Secondary Flows in Steel Casting
325(2)
11.1.5 The Role of Ekman Pumping for Non-Ferrous Metals
327(5)
11.2 Magnetic Damping Using Static Fields
332(19)
11.2.1 Metallurgical Applications
332(2)
11.2.2 The Need to Conserve Momentum in the Face of Joule Dissipation
334(3)
11.2.3 The Magnetic Damping of Submerged Jets
337(5)
11.2.4 The Magnetic Damping of Vortices
342(9)
12 Axisymmetric Flows Driven by the Injection of Current
351(23)
12.1 The Need to Purify Metal for Critical Aircraft Parts: Vacuum-Arc Remelting
351(3)
12.2 A Model Problem
354(2)
12.3 Integral Constraints and the Work Done by the Lorentz Force
356(3)
12.4 Structure and Scaling of the Flow
359(5)
12.4.1 Confined versus Unconfined Domains
359(2)
12.4.2 Shercliff's Solution for Unconfined Domains
361(2)
12.4.3 Confined Flows
363(1)
12.5 The Influence of Buoyancy
364(2)
12.6 The Apparent Spontaneous Growth of Swirl
366(3)
12.6.1 An Extraordinary Experiment
366(2)
12.6.2 But There Is no Spontaneous Growth of Swirl!
368(1)
12.6.3 Flaws in Traditional Theories Predicting a Spontaneous Growth of Swirl
369(1)
12.7 Poloidal Suppression versus Spontaneous Swirl
369(5)
13 MHD Instabilities in Aluminium Reduction Cells
374(25)
13.1 The Prohibitive Cost of Reducing Alumina to Aluminium
374(3)
13.1.1 Early Attempts to Produce Aluminium by Electrolysis
374(2)
13.1.2 An Instability in Modern Reduction Cells and Its Financial consequences
376(1)
13.2 Attempts to Model Unstable Interfacial Waves in Reduction Cells
377(2)
13.3 A Simple Mechanical Analogue for the Instability
379(5)
13.4 Simplifying Assumptions and a Model Problem
384(2)
13.5 A Shallow-Water Wave Equation for the Model Problem
386(4)
13.5.1 The Shallow-Water Wave Equations
386(3)
13.5.2 Key Dimensionless Groups
389(1)
13.6 Solutions of the Wave Equation
390(7)
13.6.1 Travelling Waves
390(1)
13.6.2 Standing Waves in Circular Domains
391(1)
13.6.3 Standing Waves in Rectangular Domains
392(5)
13.7 Implications for Cell Design and Potential Routes to Saving Energy
397(1)
Exercises
398(1)
Part IV Applications In Physics 399(142)
14 The Geodynamo
401(81)
14.1 Why Do We Need a Dynamo Theory for the Earth?
401(3)
14.2 Sources of Convection, Reversals and Key Dimensionless Groups
404(6)
14.2.1 The Structure of the Earth and Sources of Convection
404(1)
14.2.2 Field Structure and Reversals
405(3)
14.2.3 Key Dimensionless Groups
408(2)
14.3 A Comparison with the Other Planets
410(6)
14.3.1 The Properties of the Other Planets
410(3)
14.3.2 Trends in the Strengths of the Planetary Dipoles: Scaling Laws
413(3)
14.4 Tentative Constraints on Planetary Dynamo Theories
416(2)
14.5 Elementary Kinematic Theory: Phenomena, Theorems and Dynamo Types
418(22)
14.5.1 A Survey: Six Important Kinematic Results
418(3)
14.5.2 A Large Magnetic Reynolds Number Is Required
421(1)
14.5.3 Differential Rotation in the Core and the Omega-Effect
422(5)
14.5.4 An Axisymmetric Dynamo Is not Possible: Cowling's Theorem
427(2)
14.5.5 An Evolution Equation for the Axial Field
429(2)
14.5.6 A Glimpse at Parker's Helical Dynamo Mechanism
431(5)
14.5.7 Different Classes of Planetary Dynamo
436(4)
14.6 Building on Parker's Helical Lift-and-Twist Mechanism
440(10)
14.6.1 Mean-Field Electrodynamics
440(2)
14.6.2 A More Careful Look at the a-Effect
442(4)
14.6.3 Exact Integrals Relating the Large-Scale Field to the Small-Scale EMF
446(2)
14.6.4 Putting the Pieces Together: A Kinematic Criterion for Dynamo Action
448(2)
14.7 The Numerical Simulations of Planetary Dynamos
450(3)
14.8 Speculative Dynamo Cartoons Based on the Numerical Simulations
453(9)
14.8.1 Searching for the Source of the North-South Asymmetry in Helicity
453(3)
14.8.2 A Speculative Weak-Field Cartoon
456(5)
14.8.3 A Speculative Strong-Field Cartoon
461(1)
14.9 Dynamics of the Large Scale: the Taylor Constraint
462(2)
14.10 Laboratory Dynamo Experiments
464(5)
14.10.1 Two Classic Experiments
465(2)
14.10.2 More Recent Experiments
467(2)
14.11 Scaling Laws for Planetary Dynamos (Reprise)
469(3)
Exercises
472(10)
15 Stellar Magnetism
482(32)
15.1 The Dynamic Sun
483(13)
15.1.1 The Sun's Interior and Atmosphere
483(3)
15.1.2 Is There a Solar Dynamo?
486(1)
15.1.3 Sunspots and the 11-Year Solar Cycle
487(1)
15.1.4 The Location of the Solar Dynamo and Dynamo Cartoons
488(4)
15.1.5 Prominences, Flares and Coronal Mass ejections
492(4)
15.2 The Solar Wind
496(5)
15.2.1 Why Is There a Solar Wind?
496(2)
15.2.2 Parker's Model of the Solar Wind
498(3)
15.3 Accretion Discs
501(13)
15.3.1 The Basic Properties of Accretion Discs
502(5)
15.3.2 The Standard Model of Accretion Discs
507(5)
15.3.3 The Chandrasekhar-Velikhov Instability Revisited
512(2)
16 Plasma Containment in Fusion Reactors
514(27)
16.1 The Quest for Controlled Fusion Power
514(1)
16.2 The Requirements for Controlled Nuclear Fusion
515(2)
16.3 Magnetic Confinement and the Instability of Fusion Plasmas
517(15)
16.3.1 The Topology of Confinement
517(1)
16.3.2 Sausage-Mode and Kink Instabilities Revisited
518(6)
16.3.3 Axisymmetric Internal Modes
524(2)
16.3.4 Interchange and Ballooning Modes
526(6)
16.4 The Development of Tokamak Reactors
532(4)
16.5 Tritium Breeding and Heat Extraction: MHD Channel Flow Revisited
536(3)
Exercises
539
Appendices
Appendix A Vector Identities and Theorems
541(2)
Appendix B Physical Properties of Liquid Metals
543(1)
References 544(7)
Index 551
P. A. Davidson is a professor in the Department of Engineering at the University of Cambridge. He has authored over 100 publications in the fields of magnetohydrodynamics and turbulence, including the books Turbulence: An Introduction for Scientists and Engineers (2015) and Turbulence in Rotating, Stratified and Electrically Conducting Fluids (2013). He is also an associate editor of the Journal of Fluid Mechanics.